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The Cyclic Category, Tor and Ext Interpretation

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Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 301)

Abstract

Simplicial objects in an arbitrary category C can be described as functors from the category of non-decreasing maps Δ op to C. Similarly one can construct a category, denoted ΔC and called Connes cyclic category, such that a cyclic object in C can be viewed as a functor from ΔC op to C. The cyclic category ΔC was first described by Connes [1983, where it is denoted Λ or ΔK] who showed how it is constructed out of Δ and the finite cyclic groups.

Keywords

Simplicial Group Symmetric Group Simplicial Module Braid Group Cyclic Module 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliographical Comments on Chapter 6

  1. Connes, A., Cohomologie cyclique et foncteurs Ext°, C. R. Acad. Sci. Paris Sér. A-B 296 (1983), 953–958. 86d: 18007MathSciNetzbMATHGoogle Scholar
  2. Loday, J.-L., Comparaison des homologies du groupe linéaire et de son algèbre de Lie, Ann. Inst. Fourier 37 (1987), 167–190. 89i: 17011MathSciNetzbMATHCrossRefGoogle Scholar
  3. Krasauskas, R.L., Lapin, S.V., Solovev, Yu. P., Dihedral homology and cohomology, Basic notions and constructions. Mat. Sb. 133:1 (1987), 25–48. 88i: 18014Google Scholar
  4. Dunn, G., Dihedral and quaternionic homology and mapping spaces, K-theory 3 (1989), 141–161.MathSciNetzbMATHCrossRefGoogle Scholar
  5. Lodder, J.M., Dihedral homology and the free loop space, Proc. London Math. Soc. 60 (1990), 201–224. 91a: 55007MathSciNetCrossRefGoogle Scholar
  6. Lodder, J.M., Cyclic homology and de Rham cohomology, Mathematische Zeitschrift 208 (1991), 489–502.MathSciNetCrossRefGoogle Scholar
  7. Fiedorowicz, Z., Loday, J.-L., Crossed simplicial groups and their associated homology, Trans. Amer. Math. Soc. 326 (1991), 57–87. 91j: 18018MathSciNetzbMATHCrossRefGoogle Scholar
  8. Krasauskas, R.L., Skew simplicial groups, Litovsk. Mat. Sb. 27 (1987) No. 1, 89–99. 88m:18022Google Scholar
  9. Loday, J.-L., Opérations sur l’homologie cyclique des algèbres commutatives, Invent. Math. 96 (1989), 205–230. 89m: 18017MathSciNetzbMATHCrossRefGoogle Scholar
  10. Burghelea, D., Fiedorowicz, Z., Gajda, W., Adams operations in Hochschild and cyclic homology of the de Rham algebra and free loop spaces, K-theory. 4 (1991), 269–287.MathSciNetzbMATHCrossRefGoogle Scholar
  11. Mccarthy, R., The cyclic homology of an exact category, preprint, Bielefeld (1992).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  1. 1.Institut de Recherche Mathématique AvancéeCentre National de la Recherche ScientifiqueStrasbourgFrance

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